波动方程解的存在性与爆破

Existence and Blowing-up of Solution of Wave Equation

根据半群理论,引进修改的能量函数,证明了具有阻尼项和力源项的四阶波动方程的初边值问题解的整体存在性.用补偿能量的方法研究了非线性阻尼项和力源项对解的爆破行为的影响.在初始能量具有足够大的负能量情况下,解在有限时间发生爆破.得到了解的爆破时间跨度的上界.

The global existence of solution to the initial-boundary value problem of a nonlinear fourthorder wave equation with a damping term and a force source term was proved based on the standard semigroup theory and by introducing a modified energy function. The effects of nonlinear damping and force source term on blowing-up of the solution were analyzed with an energy-compensation method. The solution blows up in finite time under initial energy that is negative enough. The upper bound of life span for the solution was obtained.